Coherence properties of the radiation from SASE FEL

Transcription

1 CERN Accelerator School: Free Electron Lasers and Energy Recovery Linacs (FELs and ERLs), 31 May 10 June, 2016 Coherence properties of the radiation from SASE FEL M.V. Yurkov DESY, Hamburg I. Start-up of the FEL process from shot noise: SASE FEL. II. Longitudinal coherence (temporal and spectral properties). Statistics. III. Transverse coherence. IV. Higher harmonics.

2 What we name as X-ray FEL, SASE FEL, etc. FEL stands for free electron laser. FEL amplifier stands for single-pass free electron laser amplifier. X-ray FEL / XFEL stands for x-ray free electron laser. This is FEL amplifier starting form the shot noise in the electron beam and operating in the x-ray wavelength range. SASE FEL stands for self-amplified spontaneous emission free electron laser. This quantum terminology does not reflect actual physics of the device, but is widely used. Physically SASE FEL means FEL amplifier starting from shot noise in the electron beam device which forms separate class of vacuum tube electronics. Close relative of the FEL is travelling wave tube (TWT). Slang of the FEL community usually uses x-ray FEL, XFEL, and SASE FEL as synonyms.

3 Outline I. Start-up of the FEL process from shot noise: SASE FEL. II. III. IV. Longitudinal coherence (temporal and spectral properties). Statistics. Transverse coherence. Higher harmonics.

4 Self Amplified Spontaneous Emission - SASE - FEL TTF FEL, 2001 V. Ayvazyan et al., Phys. Rev. Lett. 88(2002)10482

5 Coherent radiation of electron beams: Introduction. Example II: modulated electron bunch E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Nucl. Instrum. and Methods A539(2005)217

6 SASE FEL

7 Qualitative look at the radiation properties Longitudinal coherence is formed due to slippage effects (electromagnetic wave advances electron beam by one wavelength while electron beam passes one undulator period). Thus, typical figure of merit is relative slippage of the radiation with respect to the electron beam on a scale of field gain length coherence time. Transverse coherence is formed due to diffraction effects. Typical figure of merit is ratio of the diffraction expansion of the radiation on a scale of field gain length to the transverse size of the electron beam.

8 Qualitative look at the radiation properties spectrum power Radiation generated by SASE FEL consists of wavepackets (spikes). Typical duration of the spike is about coherence time τ c. Spectrum also exhibits spiky structure. Spectrum width is inversely proportional to the coherence time, ω ~ 1/τ c, and typical width of a spike in a spectrum is inversely proportional to the pulse duration T. Amplification process selects narrow band of the radiation, coherence time is increased, and spectrum is shrinked. Transverse coherence is improved as well due to the mode selection process.

9 SASE FEL: Group velocity of wavepackets

10 SASE FEL Radiation from SASE FEL is statistical object, thus statistical approach needs to be applied for analysis of the properties of the radiation from SASE FEL: - Nature of statistics. - Description in terms of correlation functions and probability distribution functions. - Description of averaged characteristics (ensemble averaging). Physical effects related to coherence properties: - Longitudinal coherence: slippage effects can be studied in the framework of 1D approximation - Transverse coherence: diffraction effects can be studied in the framework of full 3D model only.

11 Strict definitions of statistical characteristics

12 Outline I. Start-up of the FEL process from shot noise: SASE FEL. II. Longitudinal coherence (temporal and spectral properties). Statistics. III. IV. Transverse coherence. Higher harmonics.

13 Statistics and probability distributions z = 0.1 z sat z = 0.5 z sat z = z sat Transverse (bottom) and longitudinal (top) distributions of the radiation intensity exhibit rather chaotic behaviour.

14 Statistics and probability distributions Linear regime Saturation Deep nonlinear regime Probability distributions of the instantaneous power density (top) and of the instantaneous radiation power (bottom) look more elegant and seem to be described by simple functions.

15 Statistics and probability distributions E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, The Physics of Free Electron Lasers

16 SASE FEL, linear regime: general features

17 SASE FEL: evolution of radiation power, fluctuations, and probability distributions Average power Amplification process passes stage of exponential growth (linear regime), and then enters nonlinear regime. Probability distributions follow negative exponential distribution in linear and deep nonlinear regime. Minimum of fluctuations occurs in the saturation.

18 SASE FEL: time correlation functions and the coherence time Maximum coherence time is achieved in the end of high gain linear regime.

19 SASE FEL: Evolution of spectrum Average power Coherence time

20 SASE FEL: Wiener-Khintchine theorem

21 SASE FEL: summary of temporal and spectral properties

22 Statistics and probability distributions: Experimental results from TTF FEL/FLASH Probability distribution of the energy in the radiation pulse Probability distribution of the energy after narrow band monochromator Linear regime Linear regime Saturation Saturation V. Ayvazyan et al., Nucl. Instrum. and Methods A 507 (2003)368

23 1D Handbook: main properties of SASE FEL

24 Outline I. Start-up of the FEL process from shot noise: SASE FEL. II. Longitudinal coherence (temporal and spectral properties). Statistics. III.Transverse coherence. IV. Higher harmonics.

25 Strict definitions of statistical characteristics

26 Qualitative look at the evolution of the radiation properties in XFEL Radiation power Brilliance Degree of transverse coherence Coherence time Radiation power continues to grow along the undulator length. Brilliance reaches maximum value at the saturation point. Degree of transverse coherence and coherence time reach their maximum values in the end of exponential regime.

27 Qualitative look at the transverse coherence Thin (diffraction limited) electron beam 2πε/λ = Undulator length to saturation is limited (9 to 10 field gain length for X-ray FELs). In the case of wide electron beam (with transverse size larger than diffraction expansion of the radiation on the scale of the field gain length), the degree of transverse coherence degrades due to poor mode selection. Wide electron beam

28 Transverse coherence Degree of transverse coherence z-s intensity distribution 2πε/λ = In the case of large emittance the degree of transverse coherence degrades due to poor mode selection. For small emittances the degree of transverse coherence visibly differs from unity. This happens due to poor longitudinal coherence: radiation spikes move forward along the electron beam, and interact with those parts of the beam which have different amplitude/phase. Longitudinal coherence develops slowly with the undulator length thus preventing full transverse coherence. E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, Opt. Commun. 186(2000)185

29 SASE FEL: limitation of transverse coherence Even after finishing the transverse mode selection process the degree of transverse coherence of the radiation from SASE FEL visibly differs from unity. This is consequence of the interdependence of the longitudinal and transverse coherence. The SASE FEL has poor longitudinal coherence which develops slowly with the undulator length thus preventing a full transverse coherence.

30 Transverse coherence Degree of transverse coherence z-s intensity distribution 2πε/λ = Poor longitudinal coherence is also responsible for the fast degradation of the transverse coherence in the nonlinear regime. In the linear exponential regime group velocity of spikes is visibly less than the velocity of light due to strong interaction with the electron beam. In the nonlinear regime group velocity of spikes approaches velocity of light due to weak interaction with the electron beam. Radiation spikes move forward faster along the electron beam and start to interact with those parts of the beam which were formed due to interaction with different wavepackets. This process develops on the scale of the field gain length.

31 Self-reproducing beam radiation modes Analytical techniques are used to calculate radiation fields in the linear mode of operation, and time-dependent numerical simulation codes are used in the general case.

32 Self-reproducing FEL radiation modes Mode degeneration 32

33 Self-reproducing FEL radiation modes Mode degeneration 33 Suppression of the mode degeneration for B = 10

34 Self-reproducing FEL radiation modes Mode degeneration 34

35 FLASH: Transverse coherence and pointing stability FLASH: experiment FLASH: FAST simulations Parameter space of FLASH: Large values of diffraction parameter (B = 10-25) and cold electron beam. Mode degeneration effect is strong (gain of TEM 10 mode is of the fundamental TEM 00 ). Contribution of the first azimuthal mode to the total power is 10 to 15%. Result: unstable shape and pointing of the photon pulse.

36 Optimized x-ray FEL 36

37 Optimized XFEL at saturation 0.6 mm-mrad 0.1 nm, 17.5 GeV 1.4 mm-mrad E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, Opt. Commun. 281(2008)1179; 281(2008)4727 ; NJP, 2010 in press.

38 Optimized x-ray FEL 38

39 Transverse coherence Contribution to the total saturation power of the radiation modes with higher azimuthal indexes 1, 2, 3, 4 grows with the emittance.

40 Optimized x-ray FEL 40

41 Optimized x-ray FEL 41

42 Properties of the radiation: Optimum tapered versus untapered case 42 Power and brilliance Degree of transverse coherence Coherence time

43 Summary on transverse coherence 43 When transverse size of the electron beam exceeds diffraction limit, the mode competition effect does not provide the selection of the fundamental FEL mode, and higher order spatial modes start to contribute to the radiation power. The consequence of interference of statistically independent spatial modes are: - Degradation of transverse coherence; - Fluctuations of the shape and pointing stability of the photon beam (both, slice and full shot). - Complicated and essentially non-gaussian field distributions across the slice. These effects stems from fundamental origin -- start-up of the amplification process from the shot noise in the electron beam. They become pronouncing at the very early stage of the degradation of the transverse coherence due to the growing contribution of the azimuthally non-symmetric modes. X-ray FELs operating at short wavelengths will demonstrate degradation of the slice field patterns and the pointing stability with the increase of the parameter 2πε/λ > 1.

44 Outline I. Start-up of the FEL process from shot noise: SASE FEL. II. Longitudinal coherence (temporal and spectral properties). Statistics. III. Transverse coherence. IV.Higher harmonics.

45 XFEL with planar undulator: odd harmonics Radiation from SASE FEL with planar undulator contains visible contributions of odd harmonics, as well as incoherent radiation from undulator. Statistical properties of the odd harmonic of the radiation from SASE FEL differ significantly from those of fundamental harmonic and incoherent undulator radiation. An origin of this difference is that the process of generation of the harmonics in the SASE FEL is nonlinear transformation from the fundamental harmonic.

46 SASE FEL: Odd harmonics Average power Instantaneous power Temporal structure of the higher harmonics exhibits more spiky behavior with respect to the fundamental.

47 XFEL with planar undulator: odd harmonics Evolution of probability distributions for the 1 st and the 3 rd harmonics Linear Saturation

48 XFEL with planar undulator: odd harmonics E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, Phys. Rev. ST Accel. Beams 9(2006)030702

49 XFEL with planar undulator: odd harmonics Coherence time: 1 st, 3 rd, 5 th Average spectra: 1 st, 3 rd, 5 th

50 Optimizedf XFEL with planar undulator: odd harmonics Diffraction effects

51 Optimized XFEL with planar undulator: odd harmonics Diffraction effects

52 Summary This lecture presents an overview of the properties of the radiation from x-ray free electron lasers. Simple formulae allow one to obtain quantitative description of the SASE FEL operating in the saturation regime. For more details we address you to suggested further reading which highlights theoretical developments, up-to-date experimental activity at FLASH, LCLS, SACLA, and projects of XFELs to be realized soon: SWISS XFEL, PAL XFEL, and European XFEL. Thank you for your attention!

53 Suggested bibliography A. FEL theory: 1. E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, The Physics of Free Electron Lasers (Springer-Verlag, Berlin, 1999). 2. E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, A simple method for the determination of the structure of ultrashort relativistic electron bunches, Nucl. Instrum. and Methods A539(2005) E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Statistical properties of radiation from VUV and X-ray free electron lasers, Optics Communications 148(1998) E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Diffraction effects in the self-amplified spontaneous emission FEL, Optics Communications 186(2000) E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Statistical properties of radiation from SASE FEL driven by short electron bunches, Nucl. Instrum. and Methods A507(2003) E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Coherence properties of the radiation from X-ray free electron laser, Optics Communications, 281(2008) E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Output power and degree of transverse coherence of X-ray free electron lasers, Optics Communications, 281(2008) E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Statistical and coherence properties of radiation from x-ray free-electron lasers, New J. Phys. 12 (2010) G. Geloni et al., Coherence properties of the European XFEL, New J. Phys. 12 (2010) E.A. Schneidmiller and M.V. Yurkov, Statistical properties of the radiation from SASE FEL operating in a post-saturation regime with and without undulator tapering,, Journal of Modern Optics, Special Issue Short Wavelength Free Electron Lasers and their Interactions with Matter 2015, DOI: / E.A. Schneidmiller and M.V. Yurkov, Coherencece properties of the radiation from FLASH, Journal of Modern Optics, Special Issue Short Wavelength Free Electron Lasers and their Interactions with Matter 2015, DOI: / E.A. Schneidmiller and M.V. Yurkov, Fundamental Limitations of the SASE FEL Photon Beam Pointing Stability, Proc. FEL2015, TUP E.A. Schneidmiller and M.V. Yurkov, Transverse Coherence and Fundamental Limitatiton on the Pointing Stability of X-ray FELs, Proc. IPAC2016, MOPOW E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Properties of the third harmonic of the radiation from self-amplified spontaneous emission free electron laser, Phys. Rev. ST Accel. Beams 9(2006) P. Schmüser, M. Dohlus, J. Rossbach, C. Behrens, Free-Electron Lasers in the Ultraviolet and X-Ray Regime (Springer-Verlag, Berlin, 2014). 16. Z. Huang and K.-J. Kim, Review of x-ray free electron laser theory, Phys. Rev. ST Accel. Beams 10(2007) B. Statistical optics 1. J. Goodman, Statistical Optics, (John Wiley and Sons, New York, 1985). C. Experimental activity at DESY (TTF FEL, FLASH): 1. V. Ayvazyan et al., Generation of GW radiation pulses from a VUV free-electron laser operating in the femtosecond regime, Phys. Rev. Lett. 88(2002) V. Ayvazyan et al., First operation of a free-electron laser generating GW power radiation at 32 nm wavelength, The European Physical Journal D 37(2006) W. Ackermann et al., Operation of a free electron laser from the extreme ultraviolet to the water window, Nature Photonics, 1 (2007) M. Dohlus et al., Start-to-end simulations of SASE FEL at the TESLA Test Facility, phase 1, Nucl. Instrum. and Methods A530(2004) V. Ayvazyan et al., Study of the statistical properties of the radiation from a VUV SASE FEL operating in the femtosecond regime, Nucl. Instrum. and Methods A507(2003) R. Ischebeck et al., Study of the transverse coherence at the TTF free electron laser, Nucl. Instrum. and Methods A507(2003) E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Statistical properties of the radiation from VUV FEL at DESY operating at 30 nm wavelength in the femtosecond regime, Nucl. Instrum. and Methods A562(2006) E.A. Schneidmiller, and M.V. Yurkov, Application of Statistical Methods for Measurements of the Coherence Properties of the Radiation from SASE FEL, Proc. IPAC2016, MOPOW C. Behrens et al., Constraints on photon pulse duration from longitudinal electron beam diagnostics at a soft x-ray free-electron laser, Phys. Rev. ST Accel. Beams 15 (2012) S. Duesterer et al., Development of experimental techniques for the characterization of ultrashort photon pulses of extreme ultraviolet free-electron lasers, Phys. Rev. ST Accel. Beams 17 (2014) P. Schmüser, M. Dohlus, J. Rossbach, C. Behrens, Free-Electron Lasers in the Ultraviolet and X-Ray Regime (Springer-Verlag, Berlin, 2014). D. Experimental activity at XFELs: 1. P. Emma et al., First lasing and operation of an angstrom-wavelength free-electron laser, Nature Photonics, 4(2010) A.A. Lutman et al, Polarization control in an X-ray free-electron laser, Nature Photonics, Published online 09 May 2016, 1038/nphoton T. Ishikawa et al., A compact X-ray free-electron laser emitting in the sub-ångström region, Nature Photonics, 6(2012)540. E. XFEL projects : 1. LCLS WEB page: 2. M. Altarelli et al. (Eds.), XFEL: The European X-Ray Free-Electron Laser. Technical Design Report, Preprint DESY , DESY, Hamburg, 2006 (see also 3. J. Arthur et al., Linac Coherent Light Source (LCLS). Conceptual Design Report, SLAC- R593, Stanford, 2002 (see also 4. T. Tanaka and T. Shintake (Eds.), SCSS X-FEL Conceptual Design Report. Riken Harima Institute, Hyogo, Japan, May 2005 (see also 5. SWISSFEL WEB page: 6. PAL-XFEL: